Alignment: Overall Summary

The instructional materials reviewed for Math Expressions Grade 1 meet expectations for alignment to the CCSSM. The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and the materials connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

See Rating Scale
Understanding Gateways

Alignment

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Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
12
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
16
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Meets Expectations

Not Rated

Gateway 3:

Usability

0
22
31
38
38
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they partially meet expectations for being coherent and consistent with the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations for not assessing topics before the grade level in which the topic should be introduced. The materials assess grade-level content and, if applicable, content from earlier grades.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations that they assess grade-level content.

The materials provide an Assessment Guide for summative assessments. Within the Assessment Guide there is a Prerequisite Skills Inventory Test and Beginning of Year Test. Each of the assessments contain a correlations document between standard and question number. Within each Unit, there is a Test Form A and Test Form B with a correlations document, and a Performance Assessment with a grading rubric and sample student responses. A Middle of Year Test is located at the end of Unit 4 and an End of Year Test at the end of Unit 8, contain correlation documents.     Additionally, the Student Activity Book contains Unit Quick Quizzes and Unit Reviews.

Assessment items containing grade level content include, but are not limited to:

  • Middle of Year Test, Question 21 states, “Count the paper clips. How long is the object?” (1.MD.2)
  • Unit 5, Form A, Question 10, students solve “81 - 10” (1.NBT.6).
  • Unit 6, Form A, Question 13 states, “The children in a class vote for their favorite drink. They collect data about their favorite kinds. Each child votes. The teacher draws one circle for each vote (a table is provided). Write two questions about the data. Answer each question.” (1.MD.4)

Some above grade-level assessment item are included, but could be modified or omitted without a significant impact on the underlying structure of the instructional materials. Assessment items containing above grade-level content include:

  • Unit 8, Performance Test, Question 1 states, “Pablo has 7 apples. Then he picks 35 more. Draw a quick picture to show how many apples Pablo has now. Write a numbers sentence.” The Unit 4 Quick Check provides a similar story problem. (2.OA.1)

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations for spending a majority of instructional time on major work of the grade.

  • The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 7 out of 8, approximately 88%.
  • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 84 out of 95, approximately 88%.
  • The number of days devoted to major work (including assessments and supporting work connected to the major work) is 135 out of 150, approximately 90%.

A number of days level analysis is most representative of the instructional materials because some lessons require two days of instruction. As a result, approximately 90% of the instructional materials focus on major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
6/8
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 1 partially meet expectations for being coherent and consistent with the standards. The instructional materials have content designated for one grade level that is viable for one school year and foster coherence through connections at a single grade. The instructional materials partially meet expectations for having supporting content that engages students in the major work of the grade and being consistent with the progressions in the standards.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Grade 1 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters are connected to the major work of the grade in the lessons devoted to these standards, however, only Units 6 and 7 address supporting work standards. In the Teacher Edition, the Day at a Glance for each lesson contains a bubble identifying the mathematical content standards and mathematical practices addressed in the lesson, and can include connections between supporting and major work.

Examples include, but are not limited to:

  • In Unit 6, Lesson 1, students count the animal data in each of two groups and determine how many animals there are in all. This connects supporting standard represent and interpret data (1.MD.4) to the major work of add and subtract within 20 (1.OA.6 ).
  • In Unit 6, Lesson 4, students use data representations with three categories to compare most, fewest, and answer questions such as, “How many fewer eggs did Vanilla lay than Daisy? How many eggs did they lay altogether?” This connects supporting standard represent and interpret data (1.MD.4) to major work of solve addition/subtraction/comparing story problems within 20 (1.OA.1).
  • In Unit 7, Lesson 2, students “walk their fingers around a clock” while reading together the hour numbers from one through 12 as they touch them. This connects the supporting standard tell and write time in hours and half-hours (1.MD.3) to the major work of count to 120 starting with any number through natural connections (1.NBT.1).
  • In Unit 7, Lesson 8, students have to cut out shapes and fold them in half and then determine how many different ways they could fold the shape to make a half. This connects the supporting standard of partitioning shapes (1.G.3) with the major work of adding within 20 (1.OA.6).

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that the amount of content designated for one grade-level is viable for one year.

As designed, the instructional materials can be completed in 144 days. The Pacing Guide can be found on page I18 in the Teacher Edition. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications.

  • There are 95 lessons, and most lessons require one day of instruction.
  • The Pacing Guide notes lessons that may take two days, but this is not noted in the Day at a Glance for each lesson.
  • All eight units designate two days for Unit Assessments.
  • Unit 1 designates one day for the Prerequisite Skills Inventory Test.
  • Units designate 1-4 days for Quick Quizzes/Fluency Checks in the Students Activity Book for each Big Idea.

Materials indicate a teacher will need to spend more than 60 minutes providing math instruction daily. Teachers start the lesson with a 5-minute Quick Practice, which can also be done at another time of the day. Teaching the lesson is comprised of several activities with an estimated time ranging from a total of 40- 60 minutes.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 partially meet expectations for the materials being consistent with the progressions in the Standards. The instructional materials follow the progressions of the standards, and identify prior knowledge, however, there are grade-level standards that are not fully met.

The instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. The Teacher Edition (page I19) states, “Standards are designed around coherent progressions from grade to grade. Standards are not stand alone events; they form cohesive links to major work within and across grade levels,” in the Teacher Edition (page I12) there is a chart, A Path to Fluency: Kindergarten through Grade 6 to “help students achieve fluency as described in the Common Core State Standards.” Each unit contains a Math Background section referencing the standards progressions in text boxes, and how they relate to work of the grade. Each Unit Overview lays out how the progression of the grade moves towards standards in future grades. Examples of grade level progressions include, but are not limited to:

  • Teacher Edition, Unit 4, Unit Overview, the text box states, “In Grade 1, children will represent 2-digit numbers using concrete objects, place value cards, or drawings. In Grade 2, children will represent 2 and 3-digit numbers using math drawings.”
  • Teacher Edition, Path to Fluency, (page I12), the chart notes in Grade 1 students, “Fluently add and subtract within 20 demonstrating fluency for addition and subtraction within 10 (1.OA.6)” and in Grade 2 students, “Fluently add and subtract within 20 using mental strategies. By end of Grade 2 know from memory all sums of two one-digit numbers (2.OA.2).”
  • In Unit 6, Lesson 6, students solve comparison story problems using comparison bars to represent the problem. Compare situations are initially introduced in first grade. In a compare situation, two quantities are compared to find ‘How many more’ or ‘How many less.’

The instructional materials attend to the full intent of many grade-level standards by giving all students extensive work with grade-level problems, however, instances where the full intent of the grade-level standards are not met is evident as students have limited opportunities to engage in extensive work. The structure of the Math Expressions program provides a variety of learning opportunities for students to master the grade-level curriculum and provide extensive work with grade-level problems. Knead Knowledge through Practice ensures students gain understanding and fluency with desired methods. Daily Routines, Quick Practice, Student Practice pages, Homework practice, Remembering pages, and Math Activity Centers support the classroom learning in every lesson. Some instances are evident where the full intent of the standard is not met, and there are some lessons that would need to be omitted as they attend to future grade standards.

Examples of materials meeting full intent of the standards include, but are not limited to:

  • Unit 3, Lessons 3 through 12, Quick Practice, students count on to find the unknown partner in addition equations. For example, “2 + ? = 4” (1.OA.8).
  • Unit 4, Lesson 12, Math Activity Center for on-level, challenge, and intervention work. On-Level Resources include Activity Card 4-12 which has students write two 2-digit numbers, model the numbers with a drawing, and compare the numbers. Challenge Resources include Activity Card 4-12 which has students create four 2-digit numbers and determine which has the greatest value and which has the least value. Students needing intervention complete Activity Card 4-12 which has students represent two 2-digit numbers using base ten blocks and compare the numbers using >, <, or = (1.NBT.3).
  • Unit 6, Daily Routines, Example 83, the student leader shows the class a number with one Demonstration Secret Code Card tens card and a ones card. Then asks the students, “What is this number? How many tens and ones? What is ten more than 83? Why?” (1.NBT.2)

Instances where full intent of the standard is not met:

  • Three lessons in Unit 7 (Lessons 12, 13, 14) address standard 1.MD.1, measure lengths indirectly and by iterating length units which is major work of the grade. Within the three lessons, students measure two real objects and 13 pictures of objects with paper clips. Students are not given the opportunity to measure with different objects or to compare how the measurements are different if different measuring tools, other than paper clips are used. Supplemental work may need to be provided to meet the full intent of this standard.
  • Four lessons in Unit 4 (Lessons 3, 12, 16, 18) address standard 1.NBT.3, compare two-digit numbers using symbols. An additional comparing numbers lesson appears in Unit 8, Lesson 6, however no symbols are used for the comparisons.

One example of an above grade level lesson needing to be omitted:

  • Unit 8, Lessons 1 and 2, students are introduced to the “New Group Below” and “New Group Above” methods for vertical addition. The “New Group Above Method” is the standard algorithm which is a Grade 4 standard (4.NBT.4) and is not clearly identified as future grade level content. Throughout the Unit, students are not required to use the “New Group Above” method.

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Learning paths are identified at the beginning of each unit relating grade-level concepts to prior knowledge from earlier lessons. Examples where content is connected to prior grades includes, but is not limited to:

  • Teacher Edition, Unit 1, Learning Path in the Common Core Standards, states, “Unit 1 emphasizes the 1-more and 1-less pattern, first with counting numbers, then with finding partners, and finally with addition and subtraction. The repeated experiences in Unit 1 are a bridge from Kindergarten experiences to the embedded addends required in Unit 2 for counting on...Later in Units 2 and 3, children will extend their thinking to using strategies for adding and subtracting within 10.”
  • Teacher Edition, Unit 4, Learning Path in the Common Core Standards, the author states, “This unit builds on the work with teen numbers that began in Kindergarten. Children explore tens and ones using physical groupings and math drawings. Activities provide repeated experience in building 2-digit numbers with strong visual support. Children extend these place value concepts to adding with 1- and 2-digit numbers.”
  • Teacher Edition, Unit 7, Learning Path in the Common Core Standards, the author states, “This unit builds on the geometry and measurement concepts and knowledge that children bring from Kindergarten.”

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

The instructional materials foster coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include learning objectives visibly shaped by CCSSM cluster headings, and provide problems and activities connecting two or more clusters in a domain or two or more domains when the connections are natural and important. ​

Examples where materials include learning objectives visibly shaped by CCSSM cluster headings include, but are not limited to:

  • Each unit is broken into several “Big Ideas” shaped by the CCSSM cluster headings. For example, in Unit 3, Unknown Numbers in Addition and Subtraction, contains three Big Ideas:
    • Big Idea 1: Counting on with Addition Situations, is shaped by 1.OA.B: Understand and apply properties of operations and the relationship between addition and subtraction.
    • Big Idea 2: Counting on with Subtraction Situations, is shaped by 1.OA.B: Understand and apply properties of operations and the relationship between addition and subtraction.
    • Big Idea 3: Mixed Story Problems, is shaped by 1.OA.B: Understand and apply properties of operations and the relationship between addition and subtraction.
  • The Teacher Edition Planning Chart for each unit identifies the Big Ideas, CCSSM Domains, Clusters, and Standards for each lesson.
  • Unit 7, Big Idea 1 is designed around Grade 1 cluster heading: Tell and write time. In Lesson 5, students tell and write time to the hour and half-hour (1.MD.3).

Examples of connections between clusters and/or domains include, but are not limited to:

  • Unit 3, Lessons 1 through 5, connect 1.OA.A: Represent and solve problems involving addition, and subtraction to 1.OA.B: Understand and Apply Properties of Operations and the Relationship Between Addition and Subtraction. Students practice finding “unknown partners” as they solve, add to situations with the change unknown, and put together/take apart problems with one addend unknown.
  • Unit 7, Lessons 6 and 7, connect 1.G.A: Reason with shapes and their attributes, and 1.MD.C: Represent and interpret data. Students sort shapes based on their attributes and answer questions about how the data was sorted.
  • Unit 8, Lessons 2 and 3, connect 1.NBT.C: Use place value understanding and properties of operations to add and subtract, to 1.OA.A: Represent and Solve Problems Involving Addition and Subtraction. Students solve addition word problems requiring them to add two 2-digit numbers together.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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Gateway Two Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they partially meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. The instructional materials also do not always treat the aspects of rigor separately or together.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Materials include problems and questions that develop conceptual understanding and provide opportunities for students to independently demonstrate conceptual understanding throughout the grade where called for in the standards. The Teacher’s Edition page vii states, “Through using objects, drawings, conceptual language, and real-world situations, students build mathematical ideas that make sense to them.”

Materials utilize MathBoards (laminated boards) for students to make their own drawings to communicate their conceptual understanding. Students have access to iTools to model conceptual understanding. Math Talk activities provide “frequent opportunities for students to explain their mathematical thinking and to ask questions of other explainers deepens their understanding of concepts.” Additionally, What’s The Error activities with the Puzzled Penguin provide students the opportunity to identify errors, discuss why it is incorrect, and how to correct it. Finally, Learning Paths, found in each unit, explain how students will build understanding of concepts throughout the unit.

Examples include but are not limited to:

  • In Units 1, 2, and 3, Daily Routines activities use the 120 Poster, Count by Tens and Ones Up to a Number to help students understand place value through the use of a concrete models. Students use columns with 10 blue circles in each to show a group of 10 which is later connected to a representation using “Secret Code Cards” a version of place value cards where a two-digit number is created by placing the ones digit card on top of the “0” in the tens place card. For example, the tens card is 90, and the 5 card gets placed on top of the 0 in 90 to make 95. Using place value cards in this manner reinforces the concept of digit 9 in 90 having a value of 90 (1.NBT.2).
  • In Unit 2, the Learning Path, explains how students will build understanding of place value. “In this unit, children work with place value, representing numbers in different ways, and comparing numbers. They add two, three, or four 2-digit numbers, sometimes resulting in new tens or new hundreds with sums to 200.” (1.NBT.2)
  • In Unit 4, Lesson 9, students are introduced to adding a 1-digit number to a 2-digit number by counting on. A Number Path model, as well as 10-sticks and circles pictorial model are used as tools to build conceptual understanding. For example, the teacher says, “Make the number 38 (on the number path). Draw sticks through the 10-groups until you reach 30. How many sticks do you draw? Then make 8 dots until you reach 38. Write 38. Let’s say you want to add 5 to 38. Everyone make 5 more dots. What is the total? Did you make a new ten? Show it by drawing another 10-stick.” The Number Path model builds understanding of when we add, sometimes a new ten is created.  Students continue this practice independently in the Student Activity Book on page 170 (1.NBT.4).
  • In Unit 4 Lesson 12, “What’s The Error?,” the Puzzled Penguin illustrates an incorrect comparison of two 2-digit numbers and asks students, “Am I correct?” This student discussion builds and assesses students’ conceptual understanding of comparison (1.NBT.3).
  • Unit 4, Lesson 17, Math Talk, students play One Hundred Ants in small groups. Students come to an agreement on the number of ants playing the game. Students then draw a card and state how many more ants came. Students add more dots to their visual model and check to see if they are all in agreement (1.OA.8).

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

The instructional materials develop and provide independent opportunities for procedural skill and fluency throughout the grade-level. Math Expressions includes a Path to Fluency for each grade level. “This plan provides targeted practice in the Student Activity Books, Teacher Editions, Teacher Resource Books, Math Activity Centers, as well as Fluency Checks in the Student Activity Books” (TE I12). In Grade 1 the fluency plan contains practice problems in the Student Activity Book identified by a Path to Fluency icon, Fluency Checks, Quick Practices, Daily Routines, Count-On Cards, Games, Homework and Remembering pages, and online resources. Examples include but are not limited to:

  • Unit 1, Student Activity Book, students practice fluency within 10. Students practice equations involving addition and subtraction fluency within 5 and problems of plus and minus 1. As various strategies and pattern types are introduced, the set of equations is added to the practice pages to give students ongoing exposure and practice in order to develop fluency (1.OA.6).
  • In the Student Activity Book, during the Daily Routine - Remembering, students engage in rote counting practice throughout the units. For example, students practice numeral writing to 20 (1.NBT.1).
  • Periodic Fluency Checks assess addition and subtraction fluency within 10 are administered throughout the units beginning in Unit 2 after Lesson 4. For example, Volume 1, Fluency Check 6, page 122, students subtract within 10 (1.OA.6).
  • Unit 4, Lessons 1-8, Daily Quick Practice Routines, Add a Ten, students use the strategy of adding a ten to quickly find sums (1.NBT.2).  
  • Unit 4, Lesson 8, Student Activity Book, 167, students practice writing numbers and number words.  For example, students are given word form and asked to write the numeral and vice-versa (1.NBT.1).
  • Online Resource, Poggles MX, interactive game providing addition and subtraction fluency practice.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade-level and to independently demonstrate the use of mathematics flexibly in a variety of contexts. Opportunities for contextual problem solving and non-routine problems are found in Math Talks. Students are provided real-world problem scenarios throughout each lesson. Performance Tasks at the end of each unit, provide students the opportunity to solve real world situations. Also, Math Readers embed math learning in a context appropriate story. Finally, online games provide problem solving practice. For example:

  • Math Talks provide opportunities for students to engage in routine problems. In Unit 1, Lesson 8, students share stories with partners about each set of partners of 10. For example, “Guy: There are 9 girl cousins and 1 boy cousin in my family. Zaraya: I picked 8 red roses and 2 pink roses.”
  • Math Readers provide opportunities for students to solve word problems in a different context. Unit 4’s Reader, “Comic Books for Sale” includes subtraction story problems based on the pictures in the story.
  • Performance Tasks at the end of each unit, provide students with the opportunity to solve a real world task. For example, the Unit 6 Performance Task, students are directed, “To play a game, Celia and Anthony must first put their marbles into bags of 10. How many bags of 10 marbles can Celia fill? How many bags of 10 marbles can Anthony fill? If they put their marbles together first, can they fill the same total number of bags? Explain.” Non-routine practice occurs when students create their own story problems. In Unit 3, Lesson 12 students write their own story problems about sports. Students use information from a picture to write an addition or subtraction story problem. Students then share their story problems and solutions with the class.
  • In Unit 6, Lesson 9, Activity 2, students are shown the following statement, “Chen has 2 marbles. His friend gives him 4 marbles. Then another friend gives him more marbles.” They are then asked to explain why Chen now has more than 6 marbles (1.OA.2).
  • Online activities provide additional opportunities for students to apply mathematical knowledge and skills to real-world contexts. For example, in the In-Depth Inquiry Based Task for Unit 8, Fruit Pop Party, students plan a fruit pop party. Students use the information provided on charts to determine how many ice pops they will need for the party.

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

The instructional materials attend to conceptual understanding, procedural skill and fluency, and application independently to develop students’ mathematical understanding of a single topic/unit of study throughout the grade level materials. The three aspects of rigor can be found in the Daily Routines, Quick Practice, Math Talks, Fluency Checks, Puzzled Penguin, Lessons, and Homework. For example:

  • Fluency can be found in any of the 18 Fluency Checks. For example, Fluency Check 12 has students adding and subtracting within 20 (1.OA.6).
  • Conceptual Understanding can be found in any of the Puzzled Penguins “What’s the Error?” questions. For example, in Unit 6, Lesson 7, the teacher writes the following story problem on the board with an incorrect solution, “There are 11 ants and 7 beetles on the log. How many more ants than beetles are on the log? 11 + 7 = 18.” Students must determine if Puzzled Penguin is correct or incorrect and identify his mistake.

Examples where the aspects of rigor are treated together include, but are not limited to:

  • In Unit 1, Lesson 2, students count 1 - 10 together and hold up the appropriate number of fingers to match. Students play Five Crows in a Row by holding up five fingers and some more to represent the number the teacher says, building a conceptual understanding of five and number compositions. Students also work on procedural skill when they sequence number cards 1-10 correctly, and correctly show the number card for the number the teacher calls out. Students use the number cards which have a dot model imprinted on each, showing the number as a group of five with some more, students begin to visualize a 5-group and extra ones for each number, and the teacher writes a connecting expression “9 is 5 + 4”. Then students draw their own fives and ones representations for a given number. Lastly, students apply their understanding when they create their own story for a number as a group of five and some more. For example, “There are 8 apples. 5 of them belong to Antonio, and 3 of them belong to Megan.”
  • In Unit 2, Lesson 13, students build conceptual understanding when they write an equation to match a story, and draw a pictorial model to show, “There are 7 monkeys swinging in a tree. Then 4 of them leave. Now there are 3 monkeys swinging.” Students apply this understanding to write an equation, draw a model, solve the story problem, and discuss the reasonableness of their answers. Students are invited to share their own story problems and solutions with the class.
  • In Unit 6, Lesson 4, in the Student Activity Book, students count and record the data in each category to demonstrate procedural skill and fluency. They show conceptual understanding and engage in application when answering questions about the data, “How many more fish are there than ducks?” Students also create their own questions about the data.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
8/10
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 1 partially meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified, but the materials partially attend to the full meaning of each MP. The instructional materials also partially support the standards’ emphasis on mathematical reasoning.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade-level.

Materials clearly identify Mathematical Practices being used in each lesson and are embedded in the content to enrich the mathematics. Instructions are provided for teachers on how to implement Mathematical Practices within the lesson. No Mathematical Practice is under or over used in the materials.  While Mathematical Practices are not identified in the student materials, the Teacher Edition does provide highlighted narratives for Mathematical Practice activities found in the Student Activity Book.

Examples include, but are not limited to:

  • The Teacher Edition provides guidance on how to implement the Mathematical Practices in the Student Activity Book. For example, in Unit 6, Lesson 6, students solve 4 story problems using comparison bars. In the lesson narrative, MP8 is identified, and the teacher guidance states, “Children will notice that each problem on Student Activity Book page 261 is the same for all three quantities. In Problems 1 and 2, the difference is unknown. For Problem 3, the smaller quantity is unknown, and for Problem 4, the bigger quantity is unknown.”
  • All Mathematical Practices identified in the materials provide notes for the teacher. For example, in Unit 5, Lesson 10, teacher notes include, “MP2 Reason Abstractly and Quantitatively, ask children to look at this set of equations.  Invite a volunteer to explain how to solve them. Then solve the set as a class.”
  • The Overview of every unit contains “Common Core State Standards for Mathematical Practices in this Unit”. A table is provided that lists every Mathematical Practice along with corresponding lessons where that practice is embedded.
  • The “Using the Common Core Standards for Mathematical Practice” section contains a description of the Mathematical Practice along with examples of where to find it within the unit. For example, in Unit 8, the MP7 suggestion directs to teachers to, “Invite children to relate the stick-and-circle drawing to the written methods. Guide them to see that they add ones and ones, tens and tens, and in this example, make a new ten.”
  • Focus on the Mathematical Practices lessons are the last lesson in each unit. The lessons engage students in all eight practices, however, the practices are often over-identified. For example, in Unit 3, Lesson 12, the activities have students solve story problems about sports, write equation relationships, and explain their conclusions.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Grade 1 partially meet expectations that the instructional materials carefully attend to the full meaning of each practice standard.

The instructional materials attend to all eight Mathematical Practices. However, the instructional materials do not address the full meaning of Standard MP5 as tools are chosen for students, and there are few opportunities for students to choose tools strategically. For example:

  • In Unit 2, Lesson 8, Red Count-On Cards are introduced, and students use the cards to play the Number Quilt Game. Although the tool is appropriate for practice, the full intention of MP5 is not met because students do not have the opportunity to choose the tool they use.
  • In Unit 4, Lesson 5, students practice finding teen totals using the Green Make-a-Ten-Cards. Although the tool is appropriate for practice, the full intention of MP5 is not met because students do not have the opportunity to choose the tool they use to calculate teen totals.

Examples where materials attend to the full meaning of Mathematical Practices:

  • In Unit 3, Lesson 4, students solve 6 story problems. Problem 6 “Milena wants to put 8 balls in a box. She wants to have soccer and footballs. How many of each ball could she use? Show two answers.”  In the Teacher Edition, MP1 is identified: “Invite children to discuss how Problem 6 is different from the others they have just solved. Children may say that in the other problems, only one partner is unknown, but in Problem 6 both partners are unknown.”
  • In Unit 2, Lesson 13, students listen to a story problem, “There are 7 monkeys swinging in a tree. Then 4 of them leave. Now there are 3 monkeys swinging.” Students write the equation that represents the story, and the teacher asks them to prove that it is true. This procedure is followed with several more subtraction stories, including at least one that is false. (MP2)
  • In Unit 3, Lesson 8, students listen to a subtraction story, “We see 10 kangaroos. Then 4 of them jumped away. How many kangaroos are left?” Students draw Math Mountains to represent the story and write a corresponding subtraction equation. (MP4)
  • In Unit 5, Lesson 5, students discuss the differences and similarities between different addition problems depicted in cartoon strips. MP6 Attend To Precision guides teachers to “Invite [students] to describe what is the same and different.” (MP6)
  • In Unit 4, Lesson 13, Activity 1, students look for structure and identify relationships when adding with decade numbers “4 + 3=___” and “40 + 30=___”. (MP7)
  • In Unit 8, Lesson 2, Student Activity Book, students add a 2-digit number and a multiple of 10 and are guided to see/generalize that when they add only tens to a 2-digit number, they will not need to group ten ones into a ten. (MP8)

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

Math Talk is a critical component of the instructional materials and presents opportunities for students to use a consistent structure: Solve, Explain, Question, and Justify. Math Talk activities are identified in the Teacher Edition, and the structure is a familiar routine for students. In addition, students are presented with opportunities to use pictures to create math stories. Students need to explain how their story represents the picture. Examples include but are not limited to:

  • In Unit 2, Lesson 4, Write and Solve Equations activity, students write one true and one false equation. Partners then exchange their equations and solve them. Students are asked to rewrite the equation that is not true in a way that makes it true.
  • Unit 3, Lesson 12, students write an explanation supporting their analysis as to whether the statement “I can solve 7 - 4 = ___ with the equation 4 + ___ = 7” is true or false. 
  • In Unit 4, Lesson 18, students share reasoning as they determine the statement “19+5 < 20 True or false.” 

Puzzled Penguin problems are found throughout the materials and provide students an opportunity to correct errors in the penguin’s work. These tasks focus on error analysis, and many of the errors presented are procedural. Examples of Puzzled Penguin problems include: 

  • In Unit 7, Lesson 4, students discuss the Puzzled Penguin problem. “Draw the hour hand between the 12 and 1. Is Puzzled Penguin correct? No? What did Puzzled Penguin do wrong?” Puzzled Penguin showed the time 12:30, not 1:30. Students are expected to cross out the incorrect hour hand and discuss how they can help Puzzled Penguin. Responses should include that 1:30 means it is 30 minutes after 1:00. Children draw the correct hour hand halfway between the 1 and 2 to match the time on the digital clock.
  • Unit 2, Lesson 6, Puzzled Penguin, the teacher writes 5 + 3 = ___ on the board. The Puzzled Penguin says “I have 5. 5, 6, 7.” Students analyze the Puzzled Penguin’s thinking to identify a counting error when he counted 5 twice. 
  • In Unit 4, Lesson 12, the Puzzled Penguin writes 29 > 36. Students use their knowledge of place value and counting on to describe the error.
  • In Unit 5, Lesson 11, Activity 3 - Is This Statement True?, students discuss two equations: 70 - 10 = 60 and 60 + 10 = 70. Students then determine: “These questions have the same total. True or False?” 

The instructional materials over-identify MP3. For example, in Unit 7, Lessons 8, 9, 10, and 11 all identify MP3, but there are no activities that engage students in constructing arguments or analyzing the arguments of others.

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
1/2
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Grade 1 partially meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

There are some missed opportunities where the materials could assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others.

Missed opportunities include, but are not limited to:

  • Unit 4, Lesson 4, the MP3 teacher notes state, “Discuss the equation 9 + 4 = 13, guiding children to recognize that the total, 13, is made up of a ten and some ones.” The teacher is then guided to ask, “Look at the total. How many tens and ones are in 13? Does the total, 13, have a hidden 10 inside? What equation can you write that adds 1 ten and 3 ones? How do you know that 9 + 4 is 13? Is 9 + 4 the same as 10 + 3?” These questions do not guide the teacher in helping students construct viable arguments.
  • In Unit 4, Lesson 14, Student Activity Book page 184, Questions 15 and 16, students look at what the Puzzled Penguin wrote “50 + 4 = 90” and decide if he is correct and then help him by solving it correctly. The MP3 teacher notes state, “What did Puzzle Penguin do wrong? Guide a discussion to determine children’s understanding of the value of the tens and ones digits. Tell children to cross out the false equation and ask how they could help the Puzzled Penguin.” While the teacher notes identify MP3, the questioning does not help students develop critiquing reasoning about place value.
  • In Unit 7, Lesson 12, the MP3 teaching notes state, “Discuss the words long, longer, longest, and short, shorter, shortest with children. Tell children that longer and shorter are used when comparing two lengths.” There is no guidance to teachers on how to use comparisons with students to construct arguments. These notes to the teacher will not help guide students to construct viable arguments about length.

In addition, MP3 is over-identified in the materials. For example:

  • Unit 4, Lesson 9, identifies MP3, however there is no guidance for teachers to engage students in constructing arguments or analyzing the arguments of others.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
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Indicator Rating Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations that materials use accurate mathematical terminology.

There are instances where materials use “A classroom research-based term developed for Math Expressions.” These terms are used in the Student Activity Book. Examples include but are not limited to: 

  • “Tiny Tumblers” are used with Math Mountains. Tiny Tumblers represent an imaginative way for children to visualize the partners of a number. If the total represented on a Math Mountain is 10, 7 Tiny Tumblers might play on the left side of the mountain and 3 play on the right side to show 7 and 3 as partners of 10.
  • “Math Mountain” is a visual representation of the partners and total of a number. The total appears at the top, and the two partners that are added to produce the total are below to the right and left. 
  • “Break Apart Stick” is a simple stick, such as a coffee stirrer, children can use to help break apart numbers. Children lay out a certain number of counters and then use the Break-Apart Stick to separate the counters into two groups.
  • “Partner House” is a pictorial representation of all the sets of partners for a total.
  • “Secret Code Cards” are student cards that display the numerals 1-9, decade numbers 10-90, and 100.
  • “Step Stairs” are strips of rectangles that have dots on one side and on the other side a small number that displays the total number of rectangles.
  • “Sticks and Circles” are a visual representation of groups of tens as sticks and individual ones as circles.
  • “Switch the Partners/Switched Partners” refers to changing the order of the partners in an addition equation.
  • “New Group Above method/New Group Below method” is a strategy for multi-digit addition. The new groups are placed above the existing groups.
  • “Show All Totals Method” is a strategy for multi-digit addition. Add the tens column together and place the total under the problem. Next, add the ones column together and place the total under the tens total. Add up the tens and ones totals to find the answer.

In addition to a Glossary in the Student Activity Book, there are Teaching Notes on vocabulary and language and Vocabulary Activities in the back of the book. For example:

  • “Math Web: Make a word web for vocabulary words in a unit. Ask children to fill in the web with words, phrases, or examples that are related to the vocabulary word.”

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials distinguish between problems and exercises.

Materials provide the opportunity for students to learn new mathematics through problem solving activities. In a typical lesson, Activity 1 and Activity 2 develop the new math content of the lesson. Lessons are outlined according to an Inquiry Lesson Path based on four phases: Phase 1 Guided Introduction, Phase 2 Learning Unfolds, Phase 3 Knead Knowledge (practice stage), and Phase 4 Maintaining and Integrating Fluency. Students build mastery through practice problems/exercises. In a typical lesson, during Activity 2 and Activity 3, students complete problems in the Student Activity Book which provide practice with the math content. The purpose of each Activity within a unit is explained in the “Teaching the Lesson Section” found on the first page of each lesson.

Examples include but are not limited to:

  • In Unit 4 Lesson 6, Teaching the Lesson Section, Activity 1, Model and Find Doubles, is stated as being important because “Learning doubles helps children develop single-digit addition fluency and also becomes useful as an addition strategy.” Activity 2, Use Doubles Strategies to Add, is stated as important because “In this activity, children use doubles to create an easier equivalent problem.”
  • In the Student Activity Book, Unit 5, Lesson 1, Activity 1, children solve teen word problems to find unknown numbers and partners. In Activity 2, they build on this knowledge as they use the Make a Ten Strategy to find unknown partners, and in Activity 3, students practice the Make a Ten Strategy to find the unknown number in equations and word problems.

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials provide tasks in an intentional sequence.

The design of the assignments follows a natural progression, leading to full understanding and mastery of new mathematics. Lessons follow a consistent pattern of two or three activities per lesson. Activity 1 usually focuses on the new learning. This learning is reinforced in Activity 2, and then students practice the new learning by completing Student Activity Book pages during Activity 3. Activity 3 either reinforces the new skill, or it reviews previously learned content.

Examples include but are not limited to:

  • In Unit 2, Lesson 1, students solve addition story problems by drawing pictures and using Math Mountains to model the addition situation. In the Student Activity Book, students observe pictures of addition situations and write addition expressions to match the pictures.
  • In Unit 6, Lesson 1, students learn about sorting, counting, and recording data by sorting cards of animals into animals that do and do not have legs. In the Student Activity Book, students draw circles in a table to represent the animals from the sort. Next, students use the data in the table to answer questions about the number of animals. 
  • In Unit 8, Lesson 2, students solve a two-digit plus two-digit addition problem using ten-sticks and circles to represent the ones and tens. The teacher introduces the New Group Above and New Group Below methods for addition. These are initially modeled using numbers, but a connection is made to the ten-stick and circles drawings.

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials provide varied opportunities for students to present their mathematical knowledge.

Examples of how students produce answers and solutions include but are not limited to:

  • Modeling with drawings, Math Mountains, and equations
  • Modeling with fingers
  • Using Make-a-Ten Cards
  • Using counters, sticks, and strips of paper to model subtraction 
  • Providing story problem explanations
  • Writing story problems to represent different addition and subtraction situations 
  • Playing games like Number Grabber (TE 442)
  • Explaining their thinking as they answer Check for Understanding questions in the Student Activity Book
  • Identifying the error and correcting it (Puzzled Penguin)
  • Completing problems and exercises in the Student Activity Book
  • Completing fluency practice and checks in the Student Activity Book 
  • Using counters to model 10-groups
  • Using ten-sticks and circles to represent teen numbers
  • Completing both vertical and horizontal 120-charts

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials provide virtual and physical manipulatives that are faithful representations of the mathematical objects they represent and are connected to the written material.

Students use a variety of manipulatives including counters, Secret Code Cards, base-ten blocks, Make-a-Ten cards, square tiles, Stair Steps, and Math Mountains. Most of the manipulatives are available virtually in the itools found in ThinkCentral. Manipulatives are often connected to written methods when appropriate. 

Examples include but are not limited to:

  • Unit 6, Lesson 6, Stair Steps are used to compare two numbers. This is connected to comparison bars, which is a drawing method used for representing comparison and comparison story problems. Comparison Bars are also connected to unknown addend equations. 
  • Unit 4, Lesson 2, Secret Code Cards are used to show “that 1 ten is hiding inside” the teen number. This helps students make sense of place value language.

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials provide a visual design that is not distracting or chaotic but supports students in engaging thoughtfully with the mathematics.

Student Activity Book pages include many exercises per page, but they follow a consistent layout and do not feel cluttered because there are no extra and unnecessary pictures on the pages. Additionally, students are provided ample space to show their work. When needed, models, which are consistent with the materials used in the lesson, are included on the pages. For example, on Student Activity Book page 207, pictures that match the Make-a-Ten Cards are shown, and students match and complete the corresponding unknown addend equations. Illustrations, when included, are simple and do not distract from the math.

In the Teacher Guide, lessons follow a consistent layout, moving from one activity to another. Each Activity includes a large blue box that highlights the mathematical content and practice standards, the focus of the lesson, and materials needed. Parts of the lesson, such as MathTalk, are clearly labeled. For example, in Unit 6, Lesson 5, a MathTalk in Action box shows examples of how students might ask and answer questions about data in the class graph of favorite colors.

The digital interactive game, Poggles, includes simple, appealing characters that do not distract students as they practice addition and subtraction. Poggles are small squarish characters with animated faces whose appearance can be changed by adding hair and hats to the Poggle squares.

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
8/8
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations for supporting teacher learning and understanding of the CCSSM. The instructional materials include: quality questions to support teachers in planning and providing effective learning experiences, a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials, a teacher edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons, and explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Examples of teacher support include but are not limited to:

  • Questions for teachers to pose are consistently included in the lesson narrative. They are italicized, making them easily visible. 
  • MathTalk in Action boxes include questions for the teacher to ask and potential student responses. For example, in Unit 5, Lesson 11, the teacher is guided to ask the questions: “How do you know how many carrots the bunnies eat in all? How can you find how many carrots are in the garden to start? How can you use subtraction to show the story?”
  • Teacher Notes are also provided at the bottom of the lesson pages and include questions to deepen students understanding of the mathematics. For example, in Unit 1, Lesson 2, the Inquiry notes provide several probes to promote student thinking and discussion: “How do you know that you need a 5-group and another one to show 6? How do you know how many extra ones you need to draw after the 5-group? What numbers do you want to use for your story? Why?”
  • Teacher Notes at the bottom of lesson pages also include information about best practices to strengthen teachers questioning techniques. For example, in Unit 3, Lesson 1, the MathTalk note provides the following questions for teacher reflection: “What types of questions are you asking your students? Are you asking questions that elicit a short answer, or do you probe to learn more about children’s thinking as they tell about their work?"

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials contain a teacher’s edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Materials also, when necessary provide teacher guidance for the use of embedded technology to support and enhance student learning.

Ample guidance is provided in the Teacher Guide for planning. The Pacing Guide provides guidance for each unit. Charts show the Learning Progression for the Content Standards Across Grades for the standards addressed in the Unit. A Planning Chart for each Unit that includes Math Activity Center Resources, Big Idea Resources, and Lesson Resources is provided. The Planning Chart also includes the standards addressed in each lesson, the digital and print resources for each lesson, and the assessments for the Unit. A table of the Standards for Mathematical Practice and the lessons where each is embedded is included. Also, a Table of the Math Content Standards and the lessons where they are taught is provided. Finally, a list of Assessment, Review, and Intervention Resources for the Unit is provided.

Examples include but are not limited to:

  • Each lesson includes guidance on the focus of each Activity and why it is important. For example, in Unit 5, Lesson 5, Activity 1, Unknown Numbers in Story Problems, is stated as important because “Varying the unknown number in story problems helps children use related equations to solve for the unknown number.”
  • Each Activity includes an explanation of what the teacher should do or say and includes possible correct responses to questions posed by the teacher. 
  • Formative Assessment and Check for Understanding questions are highlighted in the Teacher Guide.
  • Math Practices are highlighted in the lesson narratives.
  • A list of questions that can be used to build a Math Talk community is included at the beginning of each Unit. 
  • Notes at the bottom of each page of the lesson narrative give useful suggestions for implementing the lesson, asking questions, acquiring vocabulary, and building concepts. For example, in Unit 6, Lesson 5, the Teaching Notes for Language and Vocabulary states, “Discuss the terms longest and shortest with the class. In Unit 7, children will revisit these terms when they order objects by length.”
  • Digital Resources for each lesson are highlighted on the first page of the lesson, and itools, which includes virtual manipulatives, are shown in the lesson narrative when it may be beneficial to use them. For example, in Unit 5, Lesson 9, a picture of itools Number Charts is shown because they may be used in the lesson.

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials contain a teacher’s edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.

Notes are provided at the bottom of each lesson narrative in the Teacher Edition to deepen teacher understanding of the mathematics and to improve instruction. Math Background Notes provide information about the math topic to deepen teacher’s understanding. Watch For! Notes provide information about potential misconceptions and things to watch for as students complete the lesson. What to Expect from Students notes provide information about how students might engage with the math and why the math is important. Building Concepts notes provide explanations of the math and how students learn.

Examples include but are not limited to:

  • Path to Fluency Charts are provided.
  • Chart of the Addition/Subtraction and Multiplication/Division problem types is provided.
  • Table of the Major Work and Major Clusters of the Grade is provided.
  • Table of the Common Core State Standards for Mathematical Content is provided.
  • Table of the Common Core State Standards for Mathematical Practice with an explanation for each Mathematical Practice is provided.
  • The Putting Research into Practice section at the beginning of each unit provides research about best practices in teaching children mathematics.
  • The Math Background section, prior to each unit, includes sections that deepen teacher knowledge of the math in the unit. Examples include Learning Path in the Common Core Standards, Help Students Avoid Common Errors, Effective Practice Routines, Relate Mathematics to the Real World, and Focus on Mathematical Practices. 
  • The Math Background section, prior to each unit, provides excerpts from the Progressions for the Common Core State Standards.
  • The Mathematical Practices section, prior to each unit, provides information on how students will engage with the Practice Standards throughout the unit.
  • A Teacher Glossary is provided.

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials contain a teacher’s edition that explains the role of the specific mathematics standards in the context of the overall series.

A Path to Fluency: Kindergarten through Grade 6 Chart is provided and highlights the fluency requirements of each grade level, activities that target fluency, and interventions for Grades 3, 4, 5, and 6. Also, a Major Work and Major Clusters of the Grade Chart for Grades K-6 is provided. Finally, for each unit, a Learning Progressions for the Common Core State Standards Chart for the domains addressed in the unit, which includes the current, prior, and next grade level standards is provided.

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 provide a list of lessons in the teacher's edition, cross-referencing the standards addressed and providing an estimated instructional time for each lesson, chapter, and unit.

Math Expressions does not include chapters, but rather units which are divided by Big Ideas, which are further divided into lessons. The Pacing Guide provides estimated instructional time for lessons and units. This Pacing Guide provides an estimated number of days for each unit, including lessons that may take two days and the number of days for assessments and quizzes. It should be noted that Lessons identified as taking two days in the Pacing Guide are not identified in the lesson narratives, nor is a breaking point indicated.

Examples include but are not limited to:

  • The Table of Contents provided in the introduction to the materials includes standards for all units’ Big Ideas.
  • The Chart of the Common Core State Standards for Mathematical Content provided identifies the lessons in which each standard will be addressed. 
  • The Chart of the Common Core State Standards for Mathematical Practice provided identifies the lessons in which each Mathematical Practice will be addressed. 
  • A Planning Chart is provided in the Overview for each unit that includes the standards that are addressed in each lesson. 
  • Charts of the Math Content Standards and Math Practice Standards is provided in the Overview for each unit. These charts include a list of each standard and the lessons where they are addressed. 
  • The Content and Practice Standards are identified on the first page of each lesson. The standards are also listed for each Activity within a lesson.

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

Family Letters for each unit are found in the Student Activity Book. These letters explain content, manipulatives students may use, and an explanation of terminology that may be unfamiliar to parents. Most units include between 1-3 Family Letters. Spanish versions of the letters are also included in the Student Activity Book.

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The Teacher Edition contains explanations of the program’s instructional approaches and research-based strategies. An Inquiry Learning Path describes the four phases of the Math Expressions classroom: Guided Introduction, Learning Unfolds, Knead Knowledge, and Maintaining and Integrating Fluency. The Putting Research into Practice pages at the beginning of each Unit explain best practices related to the content of the Unit. Excerpts from the Progressions for the Common Core State Standards are included in the Math Background section of each Unit. Research Notes are sometimes included in the Teaching Notes at the bottom of the lesson narrative in the Teacher Edition. For example, the Teaching Notes for Unit 3, Lesson 3, Activity 1 state, “The unknown partner equations are addition equations with an unknown addend. Children can solve unknown partner problems by counting on. Research has shown that this is the best way for young children to solve these problems. Later, children will learn to use the inverse operations or subtraction to solve these types of equations.”

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
10/10
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge, strategies for teachers to identify and address common student errors and misconceptions, and assessments that clearly denote which standards are being emphasized.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

Examples include but are not limited to:

  • The Assessment Guide contains a 25 question Prerequisite Skills Inventory Test, organized by Domains, and a corresponding Prerequisite Skills Inventory Test Correlation document. The correlation aligns each question with a description of the prerequisite skill addressed, as well as the DoK level of the question. This correlation document is formatted as a table so each student’s performance by question/skill can be recorded. The Prerequisite Skills Inventory Test is designed to be administered at the beginning of the school year.
  • When a student completes practice opportunities and tests in the Personal Math Trainer, all of the performance data and adaptive learning information follows each student to the next grade.
  • Quick Practice activities at the beginning of each lesson are designed to “provide opportunities for students to call to mind their prior understanding of a topic that has already been discussed in class or to begin to build a prerequisite skill for a topic that is to come later” (Teacher Edition page I4).
  • Quick Quizzes and Strategy Checks are embedded within the units to check understanding of Big Ideas prior to moving on to the next Big Idea instruction. For example, in Unit 1, Lesson 1 the Teaching Note states, “Recognition of a 5-group helps children gain understanding of the numbers 6 through 10 by forming a mental picture of those numbers. Further, research has shown that the ability to form quick mental pictures of quantities by grouping is crucial to performing mathematical operations efficiently” (Teacher Edition page 3). This understanding is assessed in the Quick Quiz and Strategy Check after Lesson 2 to be sure students develop this crucial prerequisite skill. 
  • Students take three progress monitoring assessments to assess grade level skills and concepts students have learned. The Beginning of Year test assesses concepts they will learn throughout the year, the Middle of Year Test shows progress made in the first half of the year, and the End of Year Test measures growth throughout the school year. 

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials provide support for teachers to identify and address common student errors and misconceptions.

Examples include but are not limited to:

  • Common student errors are identified for each Unit Review/Test question along with a direction on how to help students. For example, on the Unit 5 Review/Test, if a student misses Questions 4, 5, 9 or 17, the common error identified states, “Students may not understand the context of a story problem.” Teachers are directed to “Suggest that children make a drawing to show the story. This will help them make sense of the problem and determine whether they will add or subtract before finding a solution.”
  • The Math Background section of each Unit provides a narrative called “Help Students Avoid Common Errors”. 
  • Puzzled Penguin activities highlight typical student mistakes and misconceptions by challenging students to find the Puzzled Penguin’s mistake and correct it. Teachers are provided questions in order to lead classroom conversations through a MathTalk format that revolve around the mistake and its correction, helping students understand the mathematics.
  • Watch For! are teaching notes periodically found in each unit. These notes alert teachers to common misconceptions they should be on the lookout for. For example, in Unit 2, Lesson 10, the Watch For! note states, “Some children may call the answer the total. Explain that in a take-away problem, we start with the total and take away one of the partners. The answer is always the other partner.”

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Examples include but are not limited to:

  • Homework and Remembering pages provide a review of recently taught topics as well as a spiral review throughout the year. The Personal Math Trainer online platform allows students to complete homework tasks for each lesson, receive instant feedback, and  step-by-step guidance if needed.
  • Unit Review/Test and Performance Tasks for each unit are found in the Student Activity Book. The author states, You can use this Unit Review/Test as an end-of-unit review to determine if children have mastered the content of the unit. You can assess children’s knowledge with one of the forms of the Unit 1 Test in the Assessment Guide.” Teachers are provided with a Data-Driven Decision Making Table which suggests specific reteaching activities for students who incorrectly answer the correlated questions, as well as suggestions for which Standards Quiz to assign in the Personal Math Trainer which provides a personalized intervention for the student. The Performance Task includes a detailed scoring rubric which can be used to provide feedback to students.
  • The Personal Math Trainer can be used for homework practice, fluency practice, standards practice, unit pre-tests with instant feedback, and step-by-step guidance when needed. Everything a student completes in the platform helps to improve the adaptive workflow (powered by Knewton Adaptivity) for the student throughout the year.  
  • The Knewton Adaptivity, Homework with Daily Intervention and Enrichment can be used in multiple ways in the classroom. A 5-minute Warm-Up provides students with personalized review prior to the assignment. On-level and advanced students may receive less or no warm-up, as determined by Knewton. After the warm-up, the HMH pre-built assignment is given to students. A 10-minute personalized enrichment is provided for students who demonstrate mastery (95% or higher) on the assignment.  Enrichment shows students proximate, forward-looking concepts based on the assignment content.
  • Other Formative Assessment opportunities include: daily Check Understanding tasks on select Student Activity Book pages, daily observation with anecdotal notes, observations during Math Talk conversations, and analyzing student work samples and student responses in the Student Activity Book. Portfolio suggestions are also provided at the end of each unit.

Indicator 3p

Materials offer ongoing formative and summative assessments:
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Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
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Indicator Rating Details

The materials reviewed for Math Expressions Grade 1 meet the expectation for offering ongoing assessments that clearly denote which standards are being emphasized.

Examples include but are not limited to:

  • Every unit includes two versions of a Unit Assessment, Form A and Form B, found in the Assessment Guide. Both assessments provide PARCC and Smarter Balance question formats and a Standards Correlation Document which can be used to collect student performance data. This document also aligns each question to a DoK Level and Standard(s). 
  • Each unit contains a Performance Assessment which can be found in the Assessment Guide. The standards are clearly noted for the assessment as a whole, and not by specific question. 
  • Quick Quizzes are found throughout each unit and standards are clearly noted in the Teacher Edition.
  • There are three Benchmark Assessments (Beginning of the Year Inventory, Middle of the Year Inventory and End of Year Assessment) found in the Assessment Guide. Standards for these assessments are clearly noted on the Correlation Document and DoK Levels are noted. 

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Examples include but are not limited to:

  • Scoring Guides are provided for each Unit Performance Assessment found in the Assessment Guide. Each question is assigned a point value and a rubric is provided to determine Performance Levels 0-3 based on the number of points earned. Additionally, each Performance Level is further defined on a task-specific basis and indicates specifics about student understanding to assist teachers in interpreting student work. Sample student work for each Performance Level is also provided in the Assessment Guide. 
  • Answer keys for the Unit Assessments, Form A and Form B, are located in the back of the Assessment Guide. However, no guidance or suggestions for follow-up instruction are included in the Assessment Guide. 
  • The online Personal Math Trainer can be utilized to administer Beginning, Middle and End of Year Tests, Unit Assessments, and Fluency Checks. The data from these assessments is collected and analyzed, and a Personal Study Plan is prescribed through Adaptive Workflow settings (through Knewton Adaptivity) based on the data and the mastery threshold percentage established for the assessment. The primary use is for end of the unit assessments, or to provide targeted students with occasional review, intervention, and re-assessment opportunities. Students must complete an initial assignment (test). Students who do not demonstrate mastery receive a Personal Study Plan, consisting of a personalized review and intervention assignment lasting 15 minutes. After completing the Personal Study Plan, the initial assignment is given again, but numbers in the assessment are changed.

Indicator 3q

Materials encourage students to monitor their own progress.
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 do not encourage students to monitor their own progress and do not provide direction for teachers to encourage students to monitor their progress.

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
12/12
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 1 meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations, and they provide opportunities for advanced students to investigate mathematics content at greater depth. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Teachers guide students through an inquiry path to become mathematically proficient. The four stages of the path to learning are guided introduction, learning unfolds, knead knowledge through practice, and maintain fluency. As stated by the publisher, “Within the curriculum, a series of learning progressions reflect research on students’ natural learning stages when mastering concepts such as computation and problem-solving strategies. These learning stages informed the order of concepts, the sequence of units, and the positioning of topics in Math Expressions.” 

Examples include but are not limited to:

  • In Unit 2, Lesson 2, a teaching note is provided for students who have difficulty moving from pictures to abstract symbols when adding. Teachers are instructed to “Suggest that they draw something very simple that reminds them of the objects they are adding, instead of drawing circles.” 
  • In Unit 3, Lesson 9, students solve and discuss addition/subtraction story problems. Prompts are given for EL students at three different levels: emerging, expanding, and bridging. The prompt states, “Write at the start on the board. ‘At the start’ means ‘at the beginning '. Write ___ + 2 = 3. Point out the unknown box at the start of the equation.” Emerging: “The unknown is at the start of the equation. Ask children to repeat.” Expanding: “Where is the unknown?” Bridging: “Where is the unknown in the equation?”
  • In Unit 6, Lesson 6, a teaching note is provided on what to expect from students when solving problems with comparison bars and alternative methods. Teachers are instructed to “Encourage children to also make comparison drawings with matching lines to solve the problems on Student Activity Book pages 261 and 262. Many children may also benefit from solving with Stair Steps as well.”

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meet expectations that materials provide teachers with strategies for meeting the needs of a range of learners.

Examples include but are not limited to:

  • An explanation of differentiated instruction is provided in the Teacher Edition.
  • A list of intervention resources is provided for each unit in the Unit Overview Assessment.
  • Math Activity Centers resources for on-level, challenge, and intervention are provided for each unit’s lessons. 
  • Teaching notes for English Learners are provided for emerging, expanding, and bridging students and are provided for each unit’s lessons.
  • Some lessons have Differentiated Instruction notes provided for universal access/extra help.

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meets expectations that materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations.

MathTalks provide “an inquiry environment that encourages constructive discussion of problem-solving methods through well-defined classroom activity structures. . . comprises four components: questioning, explaining math thinking, contributing math ideas, and taking responsibility for learning” (Teacher Edition page I3). Initially teachers model MathTalks and then students run the MathTalk. For example in Unit 6, Lesson 7, the MathTalk instructs teachers to “Discuss how filling in the comparison bars for the three different problems is alike and how it is different. Guide children to the following observations: They are alike because you fill in two numbers and one box for each unknown.” Then teachers are provided prompts to help students determine how the problems are different.

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meets expectations that materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

Examples include but are not limited to:

  • Scaffolding of vocabulary is provided. For example, in Unit 2, Lesson 10, the words subtract and minus are reviewed for EL students. Teachers are instructed to “Write ‘9 - 5 = __’ on the board. Let’s solve this equation. Draw 9 circles. 9 minus 5. We subtract 5 from 9. Cross out the first 5 circles. Now there are 4 circles. 9 minus 5 equals 4.” 
  • Extra support is provided for EL students. For example, in Unit 7, Lesson 6, students learn that squares are special rectangles. Teachers are instructed to “Draw a rectangle on the board. Point to and label the sides and corners. Guide children to count each side and each corner with you.” 
  • Each unit lesson contains a Math Activity Center with activities and resources for students who are on-level and those needing challenge and intervention.
  • Teaching notes included in some lessons provide specific guidance for teachers to support students who are emerging, expanding, and bridging language acquisition.

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meets expectations that materials provide opportunities for advanced students to investigate mathematics content at greater depth.

Examples include but are not limited to:

  • Math Lessons contain Differentiated Instruction Math Activity Centers. Challenge Resources specify which Activity Card will challenge advanced students.
  • The online Personal Math Trainer provides personalized enrichment with learning supports.
  • Challenge worksheets for each lesson are available in print and digitally and are noted on the Differentiated Instruction page for each lesson.
  • Math Readers, books in the Math Activity Center, place math content in the context of stories and support higher levels of critical thinking. 

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 meets expectations that materials provide a balanced portrayal of various demographic and personal characteristics. 

Examples include but are not limited to:

  • Puzzled Penguin appears throughout the unit to provide opportunities to help students avoid common errors. These errors are presented as letters to students. Students teach Puzzled Penguin the correct way and explain why the penguin is wrong. 
  • Math Readers contain a variety of animals, children, and adults.

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 provide opportunities for teachers to use a variety of grouping strategies.

Examples include but are not limited to:

  • Math Activity Centers are provided at the conclusion of each lesson and students can be grouped individually, in pairs, or in groups to complete the Activity Cards. For example, in Unit 4, Lesson 18, Challenge Activity card 4-18, students work together to write and compare numbers. 
  • Math Writing Prompts are part of the Math Activity Centers and provide opportunities for students to work individually, in pairs, or in groups. For example, in Unit 1, Lesson 9, the On-Level Math Writing Prompt states, “Write a set of partners of 10. Then draw a picture about the partners of 10 you wrote. Tell the story your picture shows.” 
  • MathTalks provide various grouping structures. During Solve and Discuss, 4-5 students go to the board and solve the problem while the rest of the class is solving independently or as part of a small group consisting of 2-3 students. During Scenarios, a group of students act out a particular mathematical situation for other students to see.

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 sometimes encourage teachers to draw upon home language and culture to facilitate learning.

Family Letters for each unit are found in the Student Activity Book. Spanish versions of these letters are also included in the Student Activity Book. However, instructional materials do not encourage teachers to draw upon home language and culture to facilitate learning. English Learner notes in the Teacher Edition do not reference Spanish vocabulary to facilitate learning.

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
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Criterion Rating Details

The instructional materials reviewed for Math Expressions Grade 1: integrate technology in ways that engage students in the Mathematical Practices; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; are intended to be easily customized for individual learners; and do not include technology that provides opportunities for teachers and/or students to collaborate with each other.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

Examples include but are not limited to:

  • The Student Activity eBook provides audio, ability to submit answers online, a drawing tool for math drawings, guided practice to help students solve problems, and virtual manipulatives.
  • The Personal Math Trainer is an online adaptive assessment and personalized learning system for students. It analyzes student activity to determine strengths, weaknesses, learning style preferences, and pace. It provides a personalized learning path for students and generates reports for teachers to inform instruction.
  • The online Math Activity Center provides online differentiated instruction opportunities for practice, reteach, and challenge. Teachers can assign RTI assignments to students who struggle on Big Idea Quick Quizzes. Fluency Builders develop students’ basic facts and automaticity.
  • OSMO is an interactive gaming system for iPads to build students’ fluency and problem-solving skills. It offers physical manipulatives and provides immediate feedback.

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 are web-based and compatible with multiple internet browsers. In addition, materials are platform neutral and allow the use of tablets and mobile devices.

Web-based instructional materials for both teachers and students can be accessed using multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, both students and teachers can use multiple devices to access instructional materials (desktop computer, tablet, iPad, Smartboard, laptop, or cellphone). Students with disabilities can use mobile devices, assistive technology, or PCs to access materials. For example, non-readers have the option to have the entire text in an audio format. Additionally, the materials are platform-neutral for a variety of operating systems.

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 provide opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

Online assessments are available. Teachers have the ability to create their own assessments or customize those provided by the program. A variety of assessment types are provided: multi-step, fill in the blank, multiple-choice, or teacher-created questions. For example, teachers giving the computer adaptive test may edit the format and/or values of the text causing the corresponding complexity of the lesson to change accordingly.

The Personal Math Trainer is an online adaptive assessment and learning system of mathematical understanding and procedural skill/fluency. Teachers can identify question types, assignment type, or standard tested. Once students have completed the task or assessment, various charts and graphs can be generated based on standards to inform instruction. Reports are available for individual students and the entire class.

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.

Teachers can manipulate the Personal Math Trainer to create learning experiences for students targeting their needs. Additionally, teachers can create lesson materials that are specific to the learning targets for specific unit lessons. For example, in Grade 1, students practice addition and subtraction fluency. Interactive ways to practice this skill can be found in the daily routines section, task cards, math games, and activity center in the Teacher’s Edition.

The instructional materials for Math Expressions Grade 1 can be easily customized for local use. 

Digital materials include adaptive technological innovations for teachers to personalize learning for students. Digital materials can be differentiated based on individual student’s needs. For example, when using the Personal Math Trainer, teachers can add or modify existing tasks to a student’s personalized learning path. Additionally, adaptive technology allows teachers to provide two flexible differentiated styles (Daily Intervention and Enrichment or Personal Study Plan) for students.

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0
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Indicator Rating Details

The instructional materials for Math Expressions Grade 1 do not include reference technology that provides opportunities for teachers and/or students to collaborate with each other.

Materials do not provide opportunities for students and teachers to participate in discussion groups using technology.

Additional Publication Details

Report Published Date: 09/04/2019

Report Edition: 2018

Title ISBN Edition Publisher Year
CCSS Homework and Remembering BLM Grade 1 9781328703569 Houghton Mifflin Harcourt 2018
CCSS Assessment Guide BLM Grade 1 9781328703637 Houghton Mifflin Harcourt 2018
Teacher Resource Book Grade 1 9781328703705 Houghton Mifflin Harcourt 2018
CCSS Teacher Edition Collection Grade 1 9781328741417 Houghton Mifflin Harcourt 2018
CCSS Softcover Consumable Student Activity Book Collection w/Mathboards Grade 1 9781328764249 Houghton Mifflin Harcourt 2018

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

The publisher has not submitted a response.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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